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A path-integral analysis of interacting Bose gases and loop gases
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abstract
We review some recent results on interacting Bose gases in thermal equilibrium. In particular, we study the convergence of the grand-canonical equilibrium states of such gases to their mean-field limits, which are given by the Gibbs measures of classical field theories with quartic Hartree-type self-interaction, and to the Gibbs states of classical gases of point particles. We discuss various open problems and conjectures concerning, e.g., Bose-Einstein condensation, polymers and $\vert \boldsymbol{\phi} \vert^{4}$-theory.
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Nonlocal Cubic Density Gibbs Measures from Bosonic Gibbs States with Three-Body Interactions
In d=2,3, bosonic Gibbs states with renormalized nonlocal three-body interactions converge to a nonlinear classical Gibbs measure in the high-temperature mean-field limit, including all fixed-order reduced density matrices.
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